Advanced Wigner Distribution and Ambiguity Function in the Quadratic-phase Fourier Transform Domain: Mathematical Foundations and Practical Applications
Abstract
In non-stationary signal processing, prior work has incorporated the quadratic-phase Fourier transform (QPFT) into the ambiguity function (AF) and Wigner distribution (WD) to enhance their performance. This paper introduces an advanced Wigner distribution and ambiguity function in the quadratic-phase Fourier transform domain (AWDQ/AAFQ), extending classical WD/AF formulations. Key properties, including the Moyal formula, anti-derivative property, shift, conjugation symmetry, and marginal properties, are established. Furthermore, the proposed distributions demonstrate improved effectiveness in linear frequency-modulated (LFM) signal detection. Simulation results confirm that AWDQ/AAFQ outperforms both traditional WD/AF and existing QPFT-based WD/AF methods in detection accuracy and overall performance.
Keywords
Cite
@article{arxiv.2503.16258,
title = {Advanced Wigner Distribution and Ambiguity Function in the Quadratic-phase Fourier Transform Domain: Mathematical Foundations and Practical Applications},
author = {Aamir H. Dar and Neeraj Kumar Sharma},
journal= {arXiv preprint arXiv:2503.16258},
year = {2025}
}